Index of Refraction (n = c/v)

The refractive index is a speed ratio and nothing more: the speed of light in vacuum divided by its speed in the material, with $c = 299\,792\,458$ m/s exact by definition. Because nothing outruns light in vacuum, $n \geq 1$ for ordinary transparent materials. Every refraction effect you will meet descends from this one slowing — the bending at an interface, total internal reflection, the way a prism spreads colours, the shallowness of a pool. Snell's law, the critical angle and apparent depth are all downstream of $n = c/v$, which is a good reason to be clear about what it means before using it.

Water at $n = 1.333$ carries light at $2.25 \times 10^{8}$ m/s; ordinary crown glass at 1.52 gives $1.97 \times 10^{8}$; diamond at 2.417 slows it to $1.24 \times 10^{8}$ m/s. Run it forward on a number people actually use: a single-mode fibre core has $n = 1.4682$, so $v = 2.042 \times 10^{8}$ m/s, which is 4.90 µs per kilometre. A 1000 km link therefore cannot have a round-trip latency below about 9.8 ms no matter how good the electronics get — a hard floor set by this equation, and a number every network engineer eventually learns the hard way.

It is worth being careful about what "slowing" means, because the usual telling is misleading. Individual photons always travel at $c$; there is no medium in which light itself is sluggish. What happens is that the passing electromagnetic field drives the electrons in the material, those electrons re-radiate, and the superposition of the original wave with all the re-radiated wavelets is a wave whose crests advance more slowly than $c$. The bulk speed $c/n$ is a property of that superposition, not of any individual photon. This also explains why $n$ depends on wavelength: the electrons respond more strongly near their resonances, so blue is slowed more than red. That is dispersion, it is why a prism works, and it is why "$n = 1.52$ for glass" is shorthand for the value at the sodium D line at 589 nm. BK7 crown is 1.5168 there and 1.5224 in the blue at 486 nm.

Four things to watch. The $n$ in this equation is the phase index, and $c/n$ is the phase velocity. In a region of strong dispersion the phase velocity can genuinely exceed $c$, and engineered materials with $n$ below 1 exist; no information travels faster than $c$, because signals travel at the group velocity, and this distinction is garbled in popular accounts often enough to be worth stating. Second, quoting a single index without naming a wavelength is imprecise, and it matters for anything involving colour. Third, $n$ also varies with temperature and, for gases, with pressure — air is 1.000293 at standard conditions, which is why we quietly treat air as vacuum in most problems, but that tiny residual is exactly what produces road mirages and the twinkling of stars. Finally, Snell's law needs only the ratio of two indices, so when both media are given you never need $c$ at all; this page is for the cases where the speed in the material is what you actually want.